Question

A ball of mass m collides head on with another ball and comes to rest. The second ball was initially
at rest. If the coefficient of restitution is 0.5 then find the mass of the second ball​

Answer 1

In a collision, Linear momentum of the system remains constant.

Let the mass of second ball be p.

Let the velocity of first ball before collision was v.

Let the velocity of second ball after collision be u

Momentum of the system before collision

mv + p ( 0) = mv

The first ball comes to rest after collision.

Final momentum of the system after collision.

m(0) + pu = pu

Now, Since Linear momentum is conserved.

⇒ mv = pu

Given that, Coefficient of restitution e = 0. 5.

$e = \frac{u}{ v}$

$e = 0.5 = \frac{v}{u} \\ \\ 0.5 = \frac{v}{u} \times \frac{m}{m} \\ \\ 0.5 = \frac{mv}{mu} \\ \\ 0.5 = \frac{pu}{mu} \\ \\ 0.5 = \frac{p}{m} \\ \\ p = 0.5m \\ \\ p = \frac{m}{2}$

Therefore, Mass of the second ball is m/2